Statistics I – First Analysis Project
You are part of a research team that is studying academic motivation in high school students. A question has arisen regarding the strength of the relationship between academic motivation and achievement. Some members of the team believe there is a strong positive relationship between academic motivation and achievement, while others don’t think the two variables are related much, if at all.
To provide some information relevant to this discussion, a small study was designed. A random sample of 50 high school seniors from the local school district agreed to participate. Each student filled out a measure of academic motivation and released his/her SAT-math scores to the researchers. The data for this study are provided on the following page.
The measure of academic motivation was the Peabody Academic Motivation Scale (PAMS). Studies of the reliability and validity of scores obtained from using this instrument have been favorable when the instrument was used with high school students. The possible scores range from 0 to 100. The SAT-math scores can range from 200 to 800 and have also been shown to be reasonably reliable and valid in previous studies.
For this project you should:
Analyze each of the variables individually
Analyze the relationship between the two variables
Write a one or two paragraph summary of the results
Please turn in (1) the summary, (2) the program, and (3) the output.
OBS SAT MOT |
OBS SAT MOT |
1 710 68 2 660 74 3 430 88 4 570 90 5 430 70 6 560 37 7 670 79 8 420 50 9 440 77 10 320 34 11 650 82 12 630 55 13 440 79 14 420 60 15 490 89 16 530 53 17 490 48 18 450 55 19 550 97 20 490 46 21 490 71 22 470 29 23 680 82 24 310 68 25 370 31 |
26 660 100 27 430 41 28 550 50 29 630 63 30 400 23 31 460 46 32 450 76 33 230 28 34 600 57 35 340 85 36 510 70 37 620 96 38 530 68 39 490 81 40 410 50 41 480 67 42 400 54 43 610 54 44 510 71 45 380 44 46 530 85 47 720 76 48 510 67 49 520 63 50 470 56 |
Descriptive Statistics: SAT, MOT
Variable Mean StDev CoefVar
Minimum Q1
Median Q3 Maximum Range
SAT 502.2
109.3
21.75
230.0 430.0
490.0 577.5 720.0
490.0
MOT 63.66
19.32
30.35
23.00 50.00
67.00 79.00 100.00
77.00
Variable IQR Skewness Kurtosis
SAT
147.5 0.03
-0.23
MOT
29.00 -0.18
-0.66
From the above plots we can conclude that two data come from normal distributions.
From above scatter plot, we observe that two variables are positively correlated but the relation is not so good.
This fact is also observed from the value of correlation coefficient where
Pearson correlation of SAT and MOT = 0.452.
Regression Analysis: SAT versus MOT
The regression equation is
SAT = 339 + 2.56 MOT
Predictor Coef SE Coef
T P
Constant 339.42 48.38 7.02
0.000
MOT 2.5571
0.7278 3.51 0.001
S = 98.4483 R-Sq = 20.5% R-Sq(adj) =
18.8%
Analysis of Variance
Source
DF SS
MS F
P
Regression 1 119639 119639
12.34 0.001
Residual Error 48 465219 9692
Total
49 584858
Since P-value of ANOVA test is less than 0.05 so the regression
equation is significant but only 20.5% of total variation of SAT
score is explained by MOT through this regression equation.
From normal probability plot, we observe that the residuals follow normal distribution. From residual plot we see that assumption of linearity holds since the points do not follow any definite pattern and assumption of equal variances also holds.
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